Asset allocation using a Markov process of clustered efficient frontier coefficients states

Abstract

We propose a novel asset allocation model using a Markov process of states defined by clustered efficient frontier coefficients. While most research in Markov models of the market characterize regimes using return and volatility, we instead propose characterizing these states using efficient frontiers, which provide more information on the interactions of underlying assets that comprise the market. Efficient frontiers can be decomposed to their functional form, a square-root second-order polynomial defined by three coefficients, to provide a dimensionality reduction of the return vector and covariance matrix. Each month, the proposed model hierarchically clusters the monthly coefficients data up to the current month, to characterize the market states, then defines a Markov process on the sequence of states. To incorporate these states into portfolio optimization, for each state, we calculate the tangency portfolio using only return data in that state. We then take the expectation of these weights for each state, weighted by the probability of transitioning from the current state to each state. To empirically validate our proposed model, we employ three sets of assets that span the market, and show that our proposed model significantly outperforms benchmark portfolios.